The Operator Hilbert Space OH and TYPE III von Neumann Algebras

Abstract

We prove that the operator Hilbert space OH does not embed completely isomorphically into the predual of a semi-finite von Neumann algebra. This complements Junge's recent result that it admits such an embedding in the non semi-finite case.

Minor improvements, a simplification, and the observation that the same result is valid with OH replaced by $(R,C{)}_{\theta }$ ($0<\theta <1$)